Grant: Discovery Grants Program - Individual

Nowadays, high throughput data arising for instance in biostatistics-especially those observed in connection with gene expression studies-and in the environmental sciences-for instance, meteorological data transmitted from satellites-must be rapidly analyzed. Innovative techniques such as those based on samples moments, which the applicant has previously advocated, or those relying on the Bayesian approach, which are discussed in several of his papers, shall be further developed and adapted to data mine such massive sets of observations. Since complex data frequently involve several variables, I also plan to extend the semi-parametric univariate moment-based density estimation techniques that I have introduced to the multivariate context. Novel multivariate data visualization techniques that would be suited to certain types of large data sets shall be proposed as well. Extant distributional results on singular quadratic forms in Gaussian and elliptically contoured vectors shall be extended to the Hermitian case and to generalized quadratic expressions, which involve random matrices in lieu of random vectors. The bivariate density estimation techniques introduced by the applicant at the last annual meeting of The International Environmentrics Society, which consists in expressing joint density estimates in terms the product of the density estimates of the marginal distributions and a polynomial adjustment whose coefficients are determined from a moment matching technique, will be extended to multivariate settings. Once evaluated at the inverse distribution functions of the marginals, such a polynomial turns out to be a copula density. This approach arguably gives rise to the most flexible type of copulae one could devise. This methodology shall be applied to colossal data sets arising from various fields of scientific investigation such as environmetrics, financial modeling, econometrics and genomic studies. Being merely based on a finite number of joint sample moments, such techniques should prove more suitable than, for instance, kernel density estimates for modeling series of observations that can be construed as ""big data"", as they readily produce density estimates in a functional form that lends itself to algebraic manipulations. Given their computational simplicity, moment-based data mining methods ought to efficiently assist researchers in detecting anomalies, patterns and dependencies in large and complex data sets. I also intend to develop software documentation and source code to facilitate the implementation of the aforementioned distributional methodologies. Additionally, monographs on the evaluation of the distribution of various types of quadratic forms and on moment-based density estimation and approximation techniques are planned.